Question: Simplify the following expression: $ q = 1 - \dfrac{-7z + 10}{z - 8} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z - 8}{z - 8}$ $ \dfrac{1}{1} \times \dfrac{z - 8}{z - 8} = \dfrac{z - 8}{z - 8} $ Therefore $ q = \dfrac{z - 8}{z - 8} - \dfrac{-7z + 10}{z - 8} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{z - 8 - (-7z + 10) }{z - 8} $ Distribute the negative sign: $q = \dfrac{z - 8 + 7z - 10}{z - 8}$ $q = \dfrac{8z - 18}{z - 8}$